Related papers: Bosonization and Lie Group Structure
Two-dimensional quantum field theories are important in many problems in physics because they contain exact symmetries and are often completely integrable. We demonstrate the power of bosonization in elucidating the structure of a…
We discuss the connection between anyons (particles with fractional statistics) and deformed Lie algebras (quantum groups). After a brief review of the main properties of anyons, we present the details of the anyonic realization of all…
An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures…
The mechanism underlying any bosonisation or fermionisation is exposed.It is shown that any local theory of fermions on a lattice in any spatial dimension greater than one is equivalent to a local theory of Ising spins coupled to a $Z_{2}$…
We show in three dimensions, using functional integral techniques, the equivalence between the partition functions of the massive Thirring model and a gauge theory with two gauge fields, to all orders in the inverse fermion mass. Detailed…
We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp.…
Double-bosonisation associates to a braided group in the category of modules of a quantum group, a new quantum group. We announce the semiclassical version of this inductive construction.
We show that our construction of realizations for Lie algebras and quantum algebras can be generalized to quantum superalgebras, too. We study an example of quantum superalgebra $U_q(gl(2/1))$ and give the boson-fermion realization with…
The article studies the extension of the internal spaces of fermion and boson second quantized fields, described by the superposition of odd (for fermions) and even (for bosons) products of the operators $\gamma^ {a}$, to strings and odd…
We bosonize fermions by identifying their occupation numbers as the binary digits of a Bose occupation number. Unlike other schemes, our method allows infinitely many fermionic oscillators to be constructed from just one bosonic oscillator.
In this work we present symmetry transformations relating bosons to fermions which cannot be represented as a supersymmetric algebra. We present a symmetry transformation relating a complex scalar and a fermion in four dimensions and…
Using the recently discovered connection between bosonization and duality transformations (hep-th/9401105 and hep-th/9403173), we give an explicit path-integral representation for the bosonization of a massive fermion coupled to a U(1)…
In this paper we present a schema for describing dualities between physical theories (Sections 2 and 3), and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory (Sections…
Quantum Algebras (q-algebras) are used to describe interactions between fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry is invoked in order to reproduce the ground state properties of systems of fermions and…
The electromagnetic characteristics of the fractional quantum Hall states are studied by formulating an effective vector-field theory that takes into account projection to the exact Landau levels from the beginning. The effective theory is…
We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the…
A simple exposition of the rarely discussed fact that a set of free boson fields describing different, i.e. kinematically different particle types can be quantized with mutual anticommutation relations is given by the explicit construction…
The main objective of this paper is to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real time formalism of Thermofield…
Bosonization provides a powerful analytical framework to deal with one-dimensional strongly interacting fermion systems, which makes it a cornerstone in quantum many-body theory. Yet, this success comes at the expense of using effective…
We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which…